A382508 -id:A382508 - cp's OEIS frontend

A381621 Sorted list of sums of 4 prices in minor currency units for a currency that has a 2-decimal minor unit, such that the riddle "sum of prices equals product of prices" has a solution, with prices expressed as floating point numbers with 2 decimals.

644, 651, 660, 663, 665, 672, 675, 675, 678, 680, 684, 684, 686, 689, 693, 693, 702, 705, 707, 707, 708, 711, 713, 714, 714, 720, 720, 720, 725, 726, 728, 728, 729, 735, 735, 735, 737, 747, 750, 752, 756, 756, 756, 756, 762, 765, 765, 765, 765, 767, 770, 770, 774, 774, 774, 777

Offset: 1

Hugo Pfoertner, Mar 04 2025

The sequence is finite with 22640 terms.

A natural number s occurs k times in the list if there exist k multisets {a,b,c,d} of natural numbers with s = a + b + c + d and 100^3*s = a*b*c*d.

			a(1) = 644 = A380887(4) because 1.25 + 1.60 + 1.75 + 1.84 = 1.25*1.60*1.75*1.84 = 6.44 is the solution with minimum sum;
a(7) = a(8) = 675 because there are 2 solutions:
  1.00 + 1.50 + 2.00 + 2.25 = 1.00*1.50*2.00*2.25 = 6.75 and
  1.20 + 1.25 + 1.80 + 2.50 = 1.20*1.25*1.80*2.50 = 6.75;
a(22) = 711 corresponds to the solution of the puzzle "The 7-Eleven" quoted from "The Guardian" in A380887.
a(22640) = 1000004000003 is the largest term, corresponding to the quadruple of prices [0.01, 0.01, 10000.01, 10000030000.00].

Hugo Pfoertner, Table of n, a(n) for n = 1..10000
Hugo Pfoertner, Solution quadruples sorted by sum, up to sum 10^5. (2025)
Hugo Pfoertner, Complete list of 22640 solution quadruples. (2025)

Cf. A380887, A381187, A381619, A382508, A382510.

A382510 a(n) is the number of solutions to the "sum equals product" riddle with n prices v_j, i.e., find positive integers v_j, v_{j+1}>=v_j such that 100^(n-1)*Sum_{k=1..n} v_k = Product_{k=1..n} v_k.

Original entry on oeis.org

1, 13, 622, 22640

Offset: 1

Hugo Pfoertner, Apr 01 2025

See A380887 and A381619 for more information.

			a(1) = 1: [100] is the only solution.
a(2) = 13: the 13 solutions are [101, 10100], [102, 5100], [104, 2600], [105, 2100], [108, 1350], [110, 1100], [116, 725], [120, 600], [125, 500], [140, 350], [150, 300], [180, 225], [200, 200].
a(3) = 622 is the number of terms of A381619.
a(4) = 22640 is the number of terms of A381621.

Cf. A380887, A381619, A381620, A381621, A382508.

Length[Solve[100*(a + b) == a*b && a > 0 && b >= a, {a, b}, Integers]] (* Computes a(2) *)

cp's OEIS Frontend

A381621 Sorted list of sums of 4 prices in minor currency units for a currency that has a 2-decimal minor unit, such that the riddle "sum of prices equals product of prices" has a solution, with prices expressed as floating point numbers with 2 decimals.

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